{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用PCA去噪 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 手写识别的例子 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "digits = datasets.load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "noisy_digits = X + np.random.normal(0, 4, size=X.shape)  #有噪音的数据集，方差较大，噪音更明显"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "example_digits = noisy_digits[y==0,:][:10]               #生成带噪音的数据集\n",
    "for num in range(1,10):\n",
    "    example_digits = np.vstack([example_digits, noisy_digits[y==num,:][:10]]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_digits.shape   #100个样本，每个样本有64位，0-9十个数字每个数字又对应了10个样本"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):             #绘图\n",
    "    fig, axes = plt.subplots(10, 10, figsize=(10, 10),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "    gridspec_kw=dict(hspace=0.1, wspace=0.1)) \n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))    \n",
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.5, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(0.5)          #保留原来的50%数据\n",
    "pca.fit(noisy_digits)\n",
    "#pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)\n",
    "plot_digits(filtered_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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